Weak Goldbach conjecture

Statement

The conjecture states that every odd integer greater than $5$ is expressible as a sum of three primes (where two or more of the primes are possibly equal).

Relation with other conjectures and facts

Stronger conjectures

• Goldbach's conjecture: This states that every even integer greater than $2$ is a sum of two primes.

Weaker conjectures and facts

• Vinogradov's theorem: This states that every sufficiently large odd integer is a sum of three odd primes. Chaohua's strengthening of Vinogradov's theorem further allows us to pick the three primes to be roughly equal.
• Schnirelmann's theorem on Goldbach's conjecture: This states that every even integer greater than $2$ is a sum of at most $300,000$ primes.